Well I am no lawyer (though I teach several) but I would say that this hypothetical situation could involve the instructor with the supervisory role and in turn possibly end up with them being somewhat liable. Definately a possibility.

Since the move executed is not a phsyical tangible object, I'm inclined to believe that the original instructor is not at fault in cases similar to the first example. While you could certainly say that technicque X should be executed the same way each time regardless of who performs it, the fact is that there are multiple factors in each execution that will make it slightly different each time around. Therefore the responsibility of executing said technique should rely only on those executing the technique and anyone immediately supervising that person.

Furthermore, since the student turned instructor moved to another city and opened up their own school, they are affectively their own boss, legally answering to no one aside from the government. Sure they may report to you for additional learning, but you legally have no say or controll over what happens in another school in another city.

Take the example to other fields of services involving passing knowledge from one person to another:

For example, after completing high school you find yourself on hard times and decide to cook meth to create some cash flow. After your arrested, the police cannot arrest nor can family of users sue your high school chemistry teacher for teaching you how to use a Bunsen Burner.

The problem with that anology is that the chemistry teacher presumably did not teach you to cook meth, and this is a hypothetical civil case, not a criminal case under which the standard of proof is beyond a reasonable doubt.

You are correct that my musing about product liability has gaping holes, but I was trying to figure out if there was any theory under which the statute of limitations could be extended beyond the customary two or three years.

Evil plaintiff's attorney would presumably argue that because 1st degree black belt was shown this move by fifth degree black belt who currently promotes his black belts and teaches a couple times at this satellite school for cash, he is responsible for allowing this dangerous martial arts technique to exist in lesser belt's curriculium and will claim.

1) Said technique was too dangerous to be taught to others and senior BB should have known this.

2) Alternately said technique was incorrectly taught, and continued to be wrongly taught by senior black belt who never corrected his earlier dangerous interpretation of this move.

3) Senior Black belt should have told lesser black belt not to teach this deadly, spine destroying move to beginner aiki bunnies. And by virtue of belting black belts at the lesser dojo has responsibility for what is in their curriculum.

4) Senior black belt did not correct negligent supervision techniques of lesser black belt such as reading NAPMA materials during class rather then paying attention to what took place on the training floor.

Now granted these allegations are bullshit but they will probably be enough to get this case into discovery when these facts will be disproven and a motion for summary judgment will get the case against senior black belt dismissed.